A test case for application of convolutional neural networks to spatio-temporal climate data: Re-identifying clustered weather patterns

Convolutional neural networks (CNNs) can potentially provide powerful tools for classifying and identifying patterns in climate and environmental data. However, because of the inherent complexities of such data, which are often spatio-temporal, chaotic, and non-stationary, the CNN algorithms must be designed/evaluated for each specific dataset and application. Yet to start, CNN, a supervised technique, requires a large labeled dataset. Labeling demands (human) expert time, which combined with the limited number of relevant examples in this area, can discourage using CNNs for new problems. To address these challenges, here we (1) Propose an effective auto-labeling strategy based on using an unsupervised clustering algorithm and evaluating the performance of CNNs in re-identifying these clusters; (2) Use this approach to label thousands of daily large-scale weather patterns over North America in the outputs of a fully-coupled climate model and show the capabilities of CNNs in re-identifying the 4 clustered regimes. The deep CNN trained with $1000$ samples or more per cluster has an accuracy of $90\%$ or better. Accuracy scales monotonically but nonlinearly with the size of the training set, e.g. reaching $94\%$ with $3000$ training samples per cluster. Effects of architecture and hyperparameters on the performance of CNNs are examined and discussed

The Universal Aspect Ratio of Vortices in Rotating Stratified Flows: Theory and Simulation

We derive a relationship for the vortex aspect ratio $\alpha$ (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt-Vaisala frequencies within the vortex $N_c$ and in the background fluid outside the vortex $\bar{N}$, the Coriolis parameter $f$, and the Rossby number $Ro$ of the vortex: $\alpha^2 = Ro(1+Ro) f^2/(N_c^2-\bar{N}^2)$. This relation is valid for cyclones and anticyclones in either the cyclostrophic or geostrophic regimes; it works with vortices in Boussinesq fluids or ideal gases, and the background density gradient need not be uniform. Our relation for $\alpha$ has many consequences for equilibrium vortices in rotating stratified flows. For example, cyclones must have $N_c^2 > \bar{N}^2$; weak anticyclones (with $|Ro| \bar{N}^2$. We verify our relation for $\alpha$ with numerical simulations of the three-dimensional Boussinesq equations for a wide variety of vortices, including: vortices that are initially in (dissipationless) equilibrium and then evolve due to an imposed weak viscous dissipation or density radiation; anticyclones created by the geostrophic adjustment of a patch of locally mixed density; cyclones created by fluid suction from a small localised region; vortices created from the remnants of the violent breakups of columnar vortices; and weakly non-axisymmetric vortices. The values of the aspect ratios of our numerically-computed vortices validate our relationship for $\alpha$, and generally they differ significantly from the values obtained from the much-cited conjecture that $\alpha = f/\bar{N}$ in quasi-geostrophic vortices.Comment: Submitted to the Journal of Fluid Mechanics. Also see the companion paper by Aubert et al. "The Universal Aspect Ratio of Vortices in Rotating Stratified Flows: Experiments and Observations" 201

Self-Replicating Three-Dimensional Vortices in Neutrally-Stable Stratified Rotating Shear Flows

A previously unknown instability creates space-filling lattices of 3D vortices in linearly-stable, rotating, stratified shear flows. The instability starts from an easily-excited critical layer. The layer intensifies by drawing energy from the background shear and rolls-up into vortices that excite new critical layers and vortices. The vortices self-similarly replicate to create lattices of turbulent vortices. The vortices persist for all time. This self-replication occurs in stratified Couette flows and in the dead zones of protoplanetary disks where it can de-stabilize Keplerian flows.Comment: Revision submitted to Physical Review Letter

An Efficient Computational Method for Thermal Radiation in Participating Media

Thermal radiation is of significant importance in a broad range of engineering applications including high-temperature and large-scale systems. Although the governing equations of thermal radiation have been known for many years, the complexities inherent in the phenomenon, such as the multidimensionality and integro-differential nature of these equations, have made it difficult to obtain an accurate, efficient, and robust computational method. Developing the finite volume radiation method in the 1990s was a significant progress but not a panacea for computational radiation. The major drawback of this method, which is common among all methods that solve for directional intensities, is its slow convergence rate in many situations which increases the solution cost dramatically. These situations include large optical thicknesses, strongly reflecting boundaries, and any other factor that causes strong directional coupling like complex geometries. Several acceleration schemes have been developed in the heat transfer and neutron transport communities to expedite the convergence and reduce the solution cost, but none of them led to a general and reliable method. Among these available schemes, the two most promising ones, the multiplicative scheme and coupled ordinates method, suffer from failing on fine grids and being very complicated for complex scattering phase functions, respectively. In this research, a new computational method, called the QL method, has been introduced. The main idea of this method is using the phase weight concept to relate the directional and average intensities and re-arranging the Radiative Transfer Equation to find a new expression for the radiant heat flux. This results in an elliptic-type equation for the average intensity at each control volume which conserves the radiant energy in all directions in the control volume. This formulation gives the QL method a great advantage to solve for the average intensity while including the directional effects. Since the directional effects are included and the radiant energy is conserved in each control volume, this method is expected to be accurate and have a good convergence rate in all conditions. The phase weight distribution required by the QL method can be provided by a method like the finite volume method or discrete ordinates method. The QL method is applied to several 1D and 2D test cases including isotropic and anisotropic scattering, black and partially reflecting boundaries, and emitting absorbing problems; and its accuracy, convergence rate, and solution cost are studied. The method has been found to be very stable and efficient, regardless of grid size and optical thickness. This method establishes very accurate predictions on the tested coarse grids and its results approach the exact solution with grid refinement